i 05863-II-T I r_,CDAD'f'lCOLLEGEUiCkl'r r OF , ENGINEERI-_-**l- g-,,,,,, ..........NG - u,_.,_nnlmL_l ,.Jr _CR_,Jr_Lc I::rfbiNl::l:l(INl_ ] HiGHALTITUDEENGINEERINGLABORATORY Techn/coR_,pl ort s [ The Reflectance and Scattering, [ of Solar Radiation by the Earth | 1967016633-002 t THE UNIVERSITY OF MICHIGAN COLLEGE OF ENGINEERING Department of Aerospace Engineering High Altitude Engineering Laboratory i i Technical Report i THE REFLECTANCE AND SCATI_ING OF SOLAP RADIATION BY THE EARTH Fred L. Bartman I" ." ORA Project 05863 s m D under contract with: NATIONAL AERONAUTICS AND SPACE ADMINISTRATION CO_T_ACTNO. NaSr-_4(03) WASHINGTON, D.C. administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR ._ February 1967 1967016633-003 _ s report was also a dissertation submitted in parti_l fulfillment of the requirements for the de- gree of Doctor of Phi!osophy in The University of Michigan, 1967. 1967016633-004 i ACKNOWLEDG_NTS 6 I The autnor wishes to thar_ all of the many people who have assisted him in this study. The advice, and help of Professor Edward S. Epstein, I Chairman of the Doctoral Committee, is particularly appreciated. The author is also grateful to Professors Leslie M. Jones, Robert M. Howe, La_Tence L. Rauch, and Aksel Wiin-Nielsen, for serving as members of the Committee and for their help and suggestions during the course of the work. i The constant interest aad encouragement of Professors Wilbur Nelson and L. M. Jones in the early stages of the work, before the Committee was Ii. formed, arealsogratefullyacknowledged. The help of all my colleagues in the High Altitude Engineering Lab- _" oratory in carrying out preparations and field operations for the balloon " flight measurements is also acknowledged. Of these, the work of Mr. r Michael Surh, on radiometez calibration, and Messrs. Leo W. Csrls, Paul A. Titus, Wan Y. Lee, and David Hartzig on field operations and radiometer data processing is particularly appreciated. i The financial support received from the National Aeronautics and Space Administration under Contract NASr-94(03) is also gratefully ac- ° knowledged. Ntur.erousdiscussions of radiometer calibrations and the man- nero _ interpretation of radiometer data with Dr. William Nordberg, Mr. William Bandeen and other members of the Staff of Goddard Space Flight r Center, and of Mr_ Frank Malinowski of Santa Barbara Research Corpora- i tion have also been very he1_ful. T 1967016633-005 TABLE OF CONTENTS Page , LIST OF TABLES v LIST OF ILLUSTRATIONS vii I ._ NOMENCLATURE xiv ABSTRACT xxiii CHAPTER I. INTRODUCTION 1 II. DEFINITIONS 9 A. The Geometry of Scatterin_ and Reflecbion 9 B. Reflectanc,_ 9 C. Scattering Jh_le lO D. Earth's Albedo ll E. Planetary Albedo, Bond's Definition 16 IIl. A REVIEW OF RESEARCH RELATED TO EARTH'S ALBEDO 23 A. Earth's Albedo from Measurements of Earthlight on the Moon 23 B. Earth's Albedo Measurements from Satellites and Spacecraft 29 C. Reflectance of the Earth's Surface 27 D. The Reflectance of Clouds 28 E. The Scattering of Solar Radiation by Air Molecules and Aerosols 28 F. Estimates of Earth's Albedo 33 G. Discussion: Models of the Earth for Albedo Purposes 33 IV. B_LOON FLIGHT MEASUREMENTS OF EARTH REFLECTANCE 36 A. Introductory Notes 36 B. The Balloon Flight Measurement System 37 C. Radiometer Measurements: Calibration and Interpretation 43 . i. Calibration of the radiometers 14"3 2. Interpretation of the radiometer data 57 D. Data Obtained on Three Flights 63 t i. The 2 June, 1962 Balloon Flight 63 2. The 26 June,1963 Balloon Flight 78 3. The i0 March, 1969 Balloon Flight 84 ,, E. Discussion of Data Obtained 92 i i. Nonisotropic earth reflectance i00 2. The wavelength dependence of earth re- i fiectance i01 1 iii 1967016633-006 L TABLE OF CONTENTS (Continued) CIIAFTER Page V, A MODEL OF THE EARTH FOR ALBEDO PURPOSES 107 A. Geometrical Characteristics 107 B. Physical Characteristics t08 C. Illustrative Example 110 - VI. CONCLUSIONS AND SUGGESTIONS FOR FURTHER RESEARCH 124 A. Conclusions 124 B. Further Research 126 APPENDIX A. EARTH'S ALBEDO FROM MEASUREMENTS OF EARTHLIGHT ON THE MOON 128 I. The Work of Dan Jon 128 2. The Work of Bakos 131 3. The Work of Dubois 137 APPENDIX B. EARTH'S ALBEDO MEASUREMenTS FROM SATELLITES AND SP_ CECRAFT 140 I. The Low Resolution Measurements 140 2. The Medium Resolution Measurements 158 3. The Mariner 2 Measurements 183 APPENDIX C. REFLECTanCE OF THE EARTH'S SURFACE 187 i. Spectral Reflectance 187 2. Angular Distribution of Reflectance 200 3. Total Directional Reflectance 209 APPENDIX D. THE REFLECTANCE OF CLOUDS 2]8 i. Spectra] Reflectance 218 2. Angular Distribution of Reflectance 218 3. Total Directional Reflectance 219 APPENDIX E. THE SCATTERING OF SOLAR RADIATION BY AIR MOLECULES AND AERObOLS 225 i. Molecular Scattering 225 2. Aerosol Scattering 232 3. Summary 237 APPENDIX F. ESTIMATES OF EARTH'S ALBEDO 238 APPENDIX G. DESCRIPTIO]_ OF COORDINATE SYSTEM8 U8ED 249 REFERENCES 250 II iv [1 196701663g-007 LIST OF TABLES Ii Tabl_ Page I. Earth's Albedo From Measurements of Earthlight on the I Moon 2h 2. Earth's Albedo Me,..surementsFrom Satellites and Space- craft 26 3. Summary of Reflectance Data For Earth Surface Features 29 Summary I 4. of Reflectance Data for Clouds 30 5. Summary of Data for Molecular and Aerosol Scattering 32 1 6. Summary of Earth Albedo Estimates 34 [," 7. Cloud Cover Viewed by Radiometer,2 June 1962 Balloon I Flight 63 8. Theoretical F-I MRIR _eflectance Measurements 10h L 9. Illustrative Example, Values of "Jk 117 i0. Illustrative(ooooG_) Example, Values of _:kJ For GILA= 180.3e 118 ii. l(12lluoost:'ativeGMT) Example, Values of _'k_ For GHA = 0.23° n9 12. Illustrative Example, Values of _ For GHA m 180.3° (ooooOMT) _ 12o i3. Illustrative Example, Values of [ For GHA = 0.23° (1200 GMT) i 121 14. Earthshine Photometer Stations 132 15. Long;itudiualVariation of Cloud Cover 135 16. Monthly Variations of the Brightness of the Earthshine 135 17. Values _f Absorptivity for Varloue Coatings i_2 18. No3 maninald 5 Characteristics of Tiros Radi_eter Channels 160 19. Nominal Characteristics of F-_ MRIR (0.2-_.O-Micron Channe_ 168 20. Final Seasonal and Annual Values of Long- and Short- Wave Radiation 182 n v II 1967016633-008 i LIST OF TABLES (.Concluded) Table Page 21. Bidirectional Luminous Reflectance of Terrain Back- grounds for Moderately High S_n 203 22. Bidirectional Luminous Reflectance of Terrain for Low Sun Angles 206 ,_3. Bidirectional Luminous Reflectance of Terrain Back- grounds Under Overcast 207 2h. Dependence of Cloud Total Reflectance on Underlying Surface 223 25. Wavelength Dependence of Normal Optical Thickness of Earth's Molecular Atmosphere Above Sea Level "._30 26. Reflectance of Solar Radiation, _ _40 27, Data Used to Obtain Albedo of Northern Hemisphere 243 28. Seasonal Distribution of Planetary Albedo Components Due to Atmosphere Sc%tterlng and Ground Reflectance 245 % I vi t,, 1967016633-009 # I LIST OF ILLUS,"_TIONS Figure Page I i. Geometry of reflection and scattering. 6 2. Distribution of reflected radiation for a perfectly I diffuse (Lambert)reflector. 9 3. Distribution of reflected radiation for imperfectly i diffusefor threereflector,angles ofi/,incidence:0(Bo,¢o,8,0¢)°, coshO°,Bandis plotted60°. I0 4. Geometry for calculating earth's albedo. 12 I 5. Planetary albedo-geometrical relations. 17 I 6. Cperfompaerisonctly diffuseof DanJohn'somogenphaseeousfunctionearth. with that of a 25 i 7. Balloon flight confi_tLration. 39 8. Balloon gondola used on 2 June,!'962balloon flight. 39 9. Airborne telemet,> ,,_ I mounted in gondola. ..... % and instrument programming unit 41 I i0. Inside _obile teiem_ry _ro,_ndstation. 42 ii. Instrument oper_tlon prc._ramfor i0 March,]965 ',_,'lon - flight, hh i 12. Calibration sour_es. 46 _ !_. TIROS #I03A radic_.,;e_,.hs._nel5 (0.55-0.75-_ ,:"m) calibration curves. 50 ," i_. TIROS #I03A radiometer ch_._.,e_._ (0o:_-5. ,_.'ton) I. calibration curves. 51 15. Calibration curves for 0.55-O.85-mieron channel of ii F-1 MRIR radicaeter. 53 16. Calibration curves for 0.2-4.0-micron channel of ii F-i MRXR radiometer. ,_ 17. SBRC F-_ _IR calibration, 0.2-4.O-micron channel. 55 [i 18. University of Michigan F-h MRIR calibration data. |. 0,2-_.O-micron channel. 56 vii I' 1967016633-010 LIST OF ILLUSTRATYONS (Contlnue4) F_ure Page 19. Weighting function, H .$J for 0.55-0.75-mlcron channel of TIROS #103A radiometer. 59 20. Weighting function, H .$J for 0.2-6.0-micron channel of TIROS #I03A radiomete_¢ ^ 60 21. Weighting funetlon, H ._ for 0.55 0.85-mlcron channcl of F-I MRI_ radlomete_ ^ 61 22. Weigbtlng function, H .¢: for C.2-4.0-micron channel of F-h MRIR radiometer, s^ ^ 62 23. Altitude-tlme curve fo,' 2 June, 1962 balloon flight. 64 24. Trajectory for 2 June, 1962 balloon flight. 64 25. Photographs of cloud co_er for 2 June, 1962 b,_lloon flight. 65 26. Bidirectional reflectance of stratocumulus clouds, p' for 0.55-0.75-micron channel of TIROS #103A radiometer, 2 Jun_ 1962 balloon fl_ght. 67 27. Bidirectional reflectance of stratocumulus clouds, p' for 0.2-5.5-micron chana_l of TIROS #103A radi_neter 2 June, 1962 balloon flight. 68 28. Bidirectional reflectance of stratocumuluc clouds as s function of sc_tterlng angle, average values. 70 29. Cor parlson of experimental measurements of bidirectiorml reflectance of stratocumulus c_oud with theoretical sin- gle scattering pattern of water cloud model. 71 ?0. Model of bidirectional reflectance pattern of strato- cumulus cloud. 72 31. T@ta directional reflectance of a stratocumulus cloud as a function of solar angle of e]evatlon.